Physically Unclonable Functions (PUFs) are a cryptographic primitive that exploit the unique physical characteristics of Integrated Circuits (ICs). A PUF can be modeled as a black-box challenge-response system. The number and size of challenge-response pairs (CRPs) supported by a PUF determine and condition its strength. Ring Oscillators (RO)-based PUF, which are one of the most implemented on FPGA, suffer from a low number and size of CRPs. In this work, we propose an innovative mechanism to expand the size of the CRPs in a RO-PUF by using multiple bits of the two ROs under comparison. To satisfy the reliability and enhance the quality of these responses, we either switch the remaining ROs that are not used for the comparison off or use them as a background noise. We validated our proposal using FPGA measurements. The results show that, with the same number of Ring Oscillators, the CRP size can be doubled with a minimum area overhead.